Quasi-Mittag-Leffler Projective Synchronization of Delayed Chaotic Fractional Order Neural Network with Mismatched Parameters
Xin Sui, Yongqing Yang · Fractal and Fractional · 2025
This paper investigates the synchronization control problem for delayed fractional-order neural networks (DFONNs) with mismatched parameters. A novel synchronization behavior termed quasi-Mittag-Leffler projective synchronization (QMLPS) is studied. The core contribution of this work lies in the following: (1) The time delay and mismatched parameters between driven and response systems are considered, which is more general. Both static controllers and adaptive controllers are designed to synchronize the DFONNs. (2) The synchronization errors are estimated, and the rate of convergence is clarified description. By using the Lyapunov stability theory and some significant fractional-order differential inequalities, some sufficient conditions for DFONNs are derived under two kinds of control methods; furthermore, the bound of synchronization errors is estimated by the Mittag-Leffler function. Quantitative numerical simulations have demonstrated the superiority of our controller. Compared to existing results, the QMLPS introduced in this paper is more general, incorporating many existing synchronization concepts. The numerical simulation section verifies the effectiveness of the theoretical results, providing several types of synchronization behaviors of the controlled system under both mismatched and matched parameter conditions, and it also demonstrates the accuracy of the theoretical estimation of synchronization error bounds.